William Sharpe, Nobel Prize winner for his early work on Modern Portfolio Theory explained quite clearly why low-cost indexing will always produce superior returns to the median active fund manager, on any time frame.

Here is his argument in a nutshell: As a group, investors will not add anything to market returns, they can trade with one another and try hard to select the best stocks, but someone will buy at the top and someone will hold the stocks that go down, so on average everyone will get the same return as the market averages, minus their costs.

Some investors will use an index strategy, and before costs they will have the same performance as the index. Other investors will use an active strategy, but obviously their performance before costs must also be, on average, the same as the index before costs. Within the group of active funds there will be winners and losers, but clearly as a group they will not do any better than the index funds - before costs.

Since active investment strategies are necessarily going to be more expensive than index strategies, the average active investor is going to have lower returns than the average index investor.

So clearly it is impossible for the average active fund to do better than the average index fund, right?

Well, this possibly hasn't quite been the case in Australia for the last ten years or so, statistics published by various fund management research houses do show that the median Australian active fund has beaten the All Ordinaries Index. This is not true of international funds and international indexes, property securities indexes, bond indexes, cash indexes or anything else that can be actively managed or indexed, only Australian shares.

(Which brings up the question, why don't these people say you should be active in Australia yet index everywhere else? There is virtually universal agreement that indexing beats active management in virtually every market sector, except maybe Australian shares, why do people still buy active international shares, property securities, bonds or cash funds? Why do these analysts, who invariably work for organisations that make their money by researching active funds, still refuse to acknowledge the success of index funds in other sectors?)

Weird huh?

The statistics favour index funds over the shorter term, for example ASSIRT data (which was published in the 2nd Quarter 2002 "Analysts' Choice Funds" newsletter by TD Waterhouse) show that in the 3 years prior to June 30 2002 only 34% of active Australian share funds beat the S&PASX200 index. The data that shows active funds outperforming is only longer term, which of course makes the data more susceptible to the biases mentioned in the next couple of paragraphs.

First of all, one could challenge the figures, there are a variety of issues that may have improved the statistics for active funds over this period.

For a start there may be a substantial survivorship bias. This means that taking a sample of 100 funds today and measuring their performance over the last decade is not a valid approach. You need to take a random sample of 100 funds from a decade ago and track their fortunes forward (not backward) in time. If one quarter of the fund managers in your second sample are no longer in business today, either because they performed so badly they went out of business, or because they were bought out or amalgamated with another fund then the absence of these terrible underperforming funds would bias the first sample upwards.

According to Dr Burton Malkiel, author of A Random Walk Down Wall Street, survivorship bias could account for a boost of 1.4%pa, making active funds as a group look much better than they really ought to. The longer term the database, the more survivorship bias will improve the results of active managers compared to indexes, if not corrected. If these analysts that are always being quoted in Money Management are not taking survivorship into account, and the bias adds anything near 1.4%, then no doubt at all index funds have beaten active funds, because the added value usually mentioned by the analysts is rarely more than a percentage point per annum. You may well stop reading this article right here, because if you ask me this is what is wrong with the figures quoted.

A variation on survivorship bias is creation bias. This is where a fund manager takes on half a dozen promising new managers and gives each of them a small amount of seed capital to start an aggressive new fund. At least one of these managers usually turns in a spectacular performance (and this might be luck as much as anything else), while the rest won't do as well. What the manager then does is wind up the poor performing funds and throw a lot of marketing support into the new fund. This fund is then advertised widely with its spectacular past performance, and investors are sucked in. This practice is common, developing small startup funds is referred to as "incubating" a new manager.

Also, perhaps the data was not size weighted. If boutique managers are outperforming the big funds (which seems to have been the case at least for the last few years), then an average that doesn't weight the managers according to size will give boutique managers more impact on the figures. Is it really fair to give Hunter Hall, Investors Mutual, PM Capital etc, all tiny fund managers with tiny funds and great performance the same weighting in your average as the giant Colonial First State or MLC funds? Clearly more investors are getting their returns from the larger funds than the smaller funds, so a properly constructed study should give more weight to the bigger funds.

After that, before you write off index managers you should consider after tax returns. The higher turnover of active funds usually reduces their tax efficiency. If you want to know which investment is most profitable to you in a practical sense you must take into account taxes. This would easily knock a percentage point or two off the total performance of active funds compared to index funds held for a longer period of time.

There have been a number of academic studies that have investigated after-tax returns. One of the best was "Is Your Alpha Big Enough to Cover Its Taxes?" by Robert H. Jeffrey & Robert D. Arnott in The Journal of Portfolio Management, Spring 1993 pp 15-25. The basic conclusion of these is that active funds in general trade so much that even when they do beat the index pre-tax they often fail to do so after tax.

Even after taking these things into account, while no doubt the amount of value that active funds have added is trimmed greatly, I'll allow for the possibility that the statistics may still show that active funds have beaten the All Ordinaries Index.

Studies done by index managers Vanguard and Dimensional Fund Advisors, as well as academics dispute the notion that active funds have beaten index funds over the longer term. They quite clearly show that the median manager from an unbiased sample of market value-weighted active funds has been beaten by the indexes. Most people ignore these figures on the grounds that index fund managers have an intrinsic interest in promoting indexing, and the academics are "ivory tower" (an accusation I have actually had directed at me from time to time by technical analysts in aus.invest).

On the other hand, not a week goes by when someone doesn't bring to my attention an article by one analyst or another showing that active funds have beaten index funds. I do think these analysts are wrong, or using rubbery data on purpose in order to promote the active funds they make their living from, but lets just go along with the theory for a while. How can active funds as a group possibly beat indexes?

The index fund may not be properly replicating the index, they might have made a few changes and unluckily the stocks they dropped were the "good ones" so this accounts for their underperformance.

Some shareholders aren't taken into account, there does exist a third type of investor apart from Australian active funds and Australian index funds. This group is so bad at investing that they systematically buy all the bad stocks that the active funds are selling, while selling all the good stocks that the fund managers are buying.

The statistics don't take into account the actively managed dollar, that the biggest funds underperform the most but the average performance of the active funds as a group is not size weighted. This would mean the worst funds are the big funds, and a few giant fund managers underperform the rest, but because smaller fund managers are more numerous, a simple non-weighted average would make it appear that active funds as a group are giving better returns on the invested dollar.

Probably all three have contributed to the situation in Australia, because the All Ordinaries Index does happen to include some stocks that are rarely traded by active managers, which means that we could well argue that there are two different markets, the index market and the market that active investors trade in, the latter excluding less liquid index stocks.

One problem is that until now, the All Ordinaries Index has been weighted by market capitalisation, as opposed to the free float market capitalisation. In October 2002, the index will be undergoing some major changes to take this into account.

The "free float" of a company is the amount of shares that are available for trading, as opposed to strategically held. An example of a stock that has a much lower free float than market capitalisation is Newscorp, a very large chunk of which is held by the Murdoch family. The Murdochs are probably going to hold on to their share of Newscorp for ever, so a free float index would subtract out the amount held by the Murdochs to calculate the amount that is actually available to investors.

What this means is that index fund investors have held a larger proportion of Newscorp than other investors. In fact, because of Newscorp's volatility and aggressive accounting, many active funds have tried to hold as little of this stock as possible. With the great drop in Newscorp's price over the last few years (from $30 a share to $8, at the time of writing), active funds have benefited from not holding as much as the index funds.

If Newscorp, and others, were overweight in the pre-free float index, then others will need to be given greater weighting in the indexes. Australian banks, which have been a very strong performer over the last decade, are widely held and hence the free float is almost the same as the market capitalisation. Stocks like NAB will receive a bigger index weighting when the index switches to free float. Since index funds were thus underweight to banks, but overweight to NCP, one can see why active funds have had an easier time beating the All Ords than they otherwise might have.

In October, the All Ords is switching to free float. Following that, active funds and index funds will have quite similar stock weightings on average, so the "Newscorp effect" won't be there.

On the other hand, even after free float is introduced, there will still be "third parties" that potentially could play the important role of buyer at the top and seller of superior securities. As long as there is an inferior group of investors out there for active fund managers to outwit, there is going to be a source of extra revenue for active funds.

Now that we're getting strategic shareholders out of the way, there are two groups apart from "Australian Active Managers" and "Australian Index Fund Managers" who potentially could be the new patsy in the stocks game.

Those groups are foreign investors and individual investors, who could buy our worst stocks after the local active managers buy the better ones.

There certainly is evidence that individual investors have poor returns, this was collected by Terry Odean, but there are two problems here. First of all, Odean has found that individual investors are actually reasonably good stock pickers, they only underperform because they trade too much and squander their selection advantage by spending it on brokerage and bid/ask spreads. Secondly, I doubt individual investors are that important, in terms of dollars invested, and thus may not really be able to take the required large losses on behalf of the professional participants.

The other group, foreign investors, is certainly a group that control enough money to take a large chunk out of local capitalisation. Offshore investors, including international index funds, own large amounts of some of our biggest stocks. If the local fund managers are better informed about local heavyweight stocks, and succeed in out-smarting international managers by selling them our lousy stocks while holding onto our better ones, then the patsy could be foreign investors. It is certainly possible, but I don't really buy that theory.

So yes, quite possibly Australian active funds have succeeded in beating the indexes, but that was to a large extent due to deficiencies in the way our indexes are constructed, and the performance of certain stocks over this time. If the stocks responsible for this discrepancy had moved the other way, then the active funds would have had underweight positions in the top performing stocks and overweight positions in the laggers.

Will this always be the case?

Well, the foreign factor is a wild card, if foreign managers invest in our markets in a substantially different manner to local fund managers then one group will outperform the other. Which group will be the better one is impossible to predict.

In October with free float being introduced, our indexes will more closely resemble the universe of stocks that active funds are investing in, so before costs the two groups of investors should have more similar returns (which means after costs index funds should look better).

By all means you can still invest in active funds if you want to, and I have included in this FAQ my opinions on how active funds can be researched, but I think that indexing in Australia probably has a better future than many give it credit for. A lot of people I know agree that indexing makes a lot of sense and that data supports the method in America and Europe, as well as for other sectors like property securities and bonds, but they think indexing doesn't work in Australia. While possibly true in the past, at least for the last decade, in my opinion once they fix up the All Ords the story will be different.